/sci/ - Science & Math

So, i was thinking about the golden ratio spiral the other day. And I thought "instead of fibonacci/lucas numbers, why not something simpler?"

If you look at the spiral in the picture, you'll notice that each curve is a perfect quarter circle, but once it goes past the quarter mark, another perfect quarter circle is draw, only 0.618 times as large.

My idea, was instead of number sequencing, we would look at the entire spiral in quarters and count from there.

The idea is that it starts from above, travel both right and down until it gets to the quarter mark, at which point it continues to travel right but less so, but now it also traveling UP. Because it changed one of it's directions, the next quarter circle is therefore smaller.

So the math goes like this. You start at top going right + down, gain right momentum slowly, and slowly LOSE down momentum.

We can imagine right as "gaining 50% of the directional pull, and down as LOSING 50% of the pull. So you comprise and get 25%. Ah, so 25% is a quarter, and subtract that from 100 and you get 75.

So if this spiral shows a car starting at 100 mph and slows down to 75 mph (completes first quarter circle), we can correlate that to the fact that it's a quarter circle.

Now, because we change direction from right+down to right+up, we cannot keep the same momentum and therefore the 1/4 circle's radius becomes shorter. So if we started dividing with quarters on the first circle, the next circle as it is smaller could be 8ths. So an 8th of 100 is 12.5.

Since we are now in the second circle, we are in the "50 -75" range.
75 - 12.5 = 62.5. That completes the second quarter circle.

62.5... is very close to 61.8. Move decimal 2 spots to left, and you have 0.618.

Certainly, not perfect, but then again an irrational golden ratio assumes things can have infinite growth/deceleration/size. That is simply not true. And you cannot show me where a perfect golden ratio is on a ruler, as you'd be searching forever and ever.